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Cluster Analysis by Mixture Identification

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Book cover Data Analysis in Astronomy

Part of the book series: Ettore Majorana International Science Series ((EMISS,volume 24))

Abstract

Clusters analysis is frequently defined as the problem of partitioning a collection of objects into groups of similar objects according to some numerical measure of similarity. A wide variety of methods for doing this have been available for quite some time. The field has been—and remains—very well documented in the open literature [see, e.g., the books by Anderberg (1973), Diday (1979), Jambu (1978), Jambu and Lebeau (1983), Sokal and Sneath (1963), and the surveys by Diday and Simon (1976), Duda and Hart (1973), Redner and Walker (1984), to cite a few]. However, permanent emergence of new technical requirements as well as recognition of the limitations of existing techniques continue fostering intensive research activity worldwide which is mirrored by a permanent flow of publications proposing new ideas and algorithms.

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References

  • Anderberg, M.R., (1973). Clusters Analysis for Application, New York: Academic Press.

    Google Scholar 

  • Baum, L.E., T. Petrie, G. Soules, and N. Weiss, (1972). A maximization technique occurring in the statistical analysis of probabilistic functions of Markov chains. Ann. Math. Statist., 41, 164–171.

    Article  MathSciNet  Google Scholar 

  • Baum, L.E., (1972). An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. Inequalities, 8, 1–8.

    MathSciNet  Google Scholar 

  • Bryant, P., (1978). Contributions to the discussion of the paper by R.E, Quandt and J.B. Ramsey. J. Amer. Statist. Assoc, 73, 748–749.

    Google Scholar 

  • Bryant, P., and J.A. Williamson, (1978). Asymptotic behavior of classification maximum likelihood estimates. Biometrika, 65, 273–281.

    Article  MATH  Google Scholar 

  • Cooper, D.B., and P.W. Cooper, (1964). Non supervised adaptive signal detection and pattern recognition. Inform. Gontr., 7, 416–444.

    Article  MATH  Google Scholar 

  • Cooper, P. W., (1967). Some topics on nonsupervised adaptive detection for multivariate normal distributions. In Computer and Information Sciences, II, 123–146, J.T. Tou ed., New York: Academic Press.

    Google Scholar 

  • Day, N.E., (1969). Estimating the components of a mixture of normal distributions. Biometrika, 56, 463–474.

    Article  MathSciNet  MATH  Google Scholar 

  • Dempster, A.P., N.M. Laird, and D.B. Rubin, (1977). Maximum likelihood estimation from incomplete data via the EM algorithm. J. Royal Statist Soc. Ser. B,39, 1–38.

    MathSciNet  MATH  Google Scholar 

  • Diday, E., and J-C. Simon, (1976). Clustering analysis. In Digital Pattern Recognition, 47–94, K.S. Fu ed. Berlin: Springer Verlag.

    Chapter  Google Scholar 

  • Diday, E., (1979). Optimisation en Classification Automatique, Rocquencourt: INRIA.

    Google Scholar 

  • Duda, R.O., and P.E. Hart, (1973). Pattern Classification and Scene Analysis, New York: Wiley

    MATH  Google Scholar 

  • Forney, G.D., Jr. (1973). The Viterbi Algorithm. Proc. IEEE, 61, 268–278.

    MathSciNet  Google Scholar 

  • Friedman, H.P., and J. Rubin, (1967). On some invariant criterion for grouping. J. Amer. Statist. Assoc, 62, 1159–1178.

    MathSciNet  Google Scholar 

  • Fukunaga, K., and T.E. Flick, (1983). Estimation of the parameters of a Gaussian mixture using the method of moments. IEEE Trans. Pattern Anal Machine Intell., PAMI-4, 410–416.

    Google Scholar 

  • Gray, R.M., (1984). Vector quantization. IEEE ASSP Magazine, 1, 4–29.

    Article  Google Scholar 

  • Jambu, M., (1978). Classification Automatique pour I’Analyse des Donnees, Paris: Dunod.

    Google Scholar 

  • Jambu, M., and M.-O. Lebeau, (1983). Cluster Analysis and Data Analysis, Amsterdam: North-Holland.

    MATH  Google Scholar 

  • Jelinek, F., and R.L. Mercer, (1980). Interpolated estimation of Markov source parameters from sparse data. In Pattern Recognition in Practice, 381–397, E.S. Gelsema and L.N. Kanal, eds., Amsterdam: North-Holland.

    Google Scholar 

  • Jelinek, F., ILL. Mercer, and L.R. Bahl, (1982). Continuous speech recognition: Statistical methods. In Handbook of Statistics 2, 549–573, P.R. Krishnaiah and L.N. Kanal, eds. Amsterdam: North-Holland.

    Google Scholar 

  • Kazakos, D., (1977), Recursive estimation of prior probability using a mixture. IEEE Trans. Inform. Theory, IT-23, 203–211.

    Google Scholar 

  • Kazakos, D., and L.D. Davisson, (1980). An improved decision directed detector. IEEE Trans. Inform. Theory, IT-26, 113–115.

    Google Scholar 

  • Kiefer, N., (1978). Discrete parameter variation: efficient estimation of a switching regression model. Econometrika, 46, 427–434.

    Article  MathSciNet  MATH  Google Scholar 

  • Levinson, S.E., L.R. Rabiner, and M.M. Sondhi, (1983). An introduction to the application of the theory of probabilistic functions of a Markov process to automatic speech recognition. B.S.T.J., 62, 1035–1074.

    MathSciNet  MATH  Google Scholar 

  • Liporace, L.A., (1982). Maximum likelihood estimation for multivariate observations of Markov sources. IEEE Trans. Inform. Theory, IT-28, 729–734.

    Google Scholar 

  • Makov U.E., and A.F.M. Smith, (1977). A quasi-Bayes unsupervised learning procedure for priors. IEEE Trans. Inform. Theory, IT-16, 761–764.

    Google Scholar 

  • Marriot, F.H.C., (1971). Practical problems in a method of cluster analysis. Biometrics, 27, 501–514.

    Article  Google Scholar 

  • Marriot, F.H.C., (1975). Separating mixtures of normal distributions. Biometrics, 81, 767–769.

    Article  Google Scholar 

  • McLachIan, G.M., (1982). The classification and mixture maximum likelihood approaches to cluster analysis. In Handbook of Statistics 2, 199–208, P.R. Krishnaiah and L.N. Kanal, eds. Amsterdam: North-Holland.

    Google Scholar 

  • Mizoguchi, R., and M. Shimura, (1975). An approach to unsupervised learning pattern classification. IEEE Trans. Gomput., C-24, 979–983.

    Google Scholar 

  • Patrick, E.A., J.P. Costello, and P.C. Monds, (1970). Decision directed estimation of a two-class boundary. IEEE Trans. Gomput., C-19, 197–205.

    Google Scholar 

  • Postaire, J-G, and C.P.A. Vasseur, (1981). An approximate solution to normal mixture identification with application to unsupervised pattern classification. IEEE Trans. Pattern Anal. Machine Intell., PAMI-S, 163–179.

    Google Scholar 

  • Quandt, R.E., and J.B. Ramsey, (1978). Estimating mixtures of normal distributions and switching regressions. J. Amer. Statist. Assoc, 73, 730–738.

    MathSciNet  MATH  Google Scholar 

  • Rabiner, L.R., S.E. Levinson, and M.M. Sondhi, (1982). On the application of vector quantization and hidden Markov models to speaker-independent, isolated word recognition. B.S.T.J., 62, 1075–1105.

    Google Scholar 

  • Redner, R.A., and H.F. Walker, (1984). Mixture densities, maximum likelihood and the EM algorithm. Siam Review, 26, 195–239.

    Article  MathSciNet  MATH  Google Scholar 

  • Sammon, J.W., (1968). An adaptive technique for multiple signal detection and identification. In Pattern Recognition, 409–439, L.N. Kanal ed. Washington: Thomson Book Cy.

    Google Scholar 

  • Sclove, S.L., (1983). Application of the conditional population-mixture model to image segmentation. IEEE Trans. Pattern Anal Machine Intell., PAMI-5, 428–433.

    Google Scholar 

  • Scott, A.J., and M.J. Symons, (1971). Clustering methods based on likelihood ratio criteria. Biometrics, 27, 387–398.

    Article  Google Scholar 

  • Sokal, R.R., and P.H.A. Sneath, (1963). Principles of Numerical Taxonomy, San Francisco: W.H. Freeman & Oy.

    Google Scholar 

  • Stanat, D.F., (1968). Unsupervised learning of mixtures of probability functions. In Pattern Recognition, 357–389, L.N. Kanal ed. Washington: Thomson Book Oy.

    Google Scholar 

  • Symons, M.J., (1981). Clustering criteria and multivariate normal mixtures. Biometrics, 37, 35–43.

    Article  MathSciNet  MATH  Google Scholar 

  • Teicher, H., (1961). Identifiability of mixtures. Ann. Math. Stat., 32, 244–248.

    Article  MathSciNet  MATH  Google Scholar 

  • Teicher, H., (1963). Identifiability of finite mixtures. Ann. Math. Stat., 34, 1265–1269.

    Article  MathSciNet  MATH  Google Scholar 

  • Teicher, H., (1967). Identifiability of mixtures of product measures. Ann. Math. Stat., 88, 1300–1302.

    Article  MathSciNet  ADS  Google Scholar 

  • Wolfe, J.H., (1970). Pattern clustering by multivariate cluster analysis. Multivariate Behavioral Research, 5, 329–350.

    Article  Google Scholar 

  • Yakovitz, S., and J. Spragins, (1968). On the identifiability of finite mixtures. Ann. Math. Stat., 39, 209–214.

    Article  Google Scholar 

  • Yakovitz, S., (1970). Unsupervised learning and the identification of finite mixtures. IEEE Trans. Inform. Theory, IT-16, 330–338.

    Google Scholar 

  • Young, T.Y., and C. Coraluppi, (1970). Stochastic estimation of a function of normal density functions using an information criterion. IEEE Trans. Inform. Theory, IT-16, 258–263.

    Google Scholar 

  • Young, T.Y., and T.W. Calvert, (1974). Glassification, Estimation and Pattern Recognition. New York: American Elsevier.

    Google Scholar 

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© 1985 Plenum Press, New York

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Devijver, P.A. (1985). Cluster Analysis by Mixture Identification. In: GesĂą, V.D., Scarsi, L., Crane, P., Friedman, J.H., Levialdi, S. (eds) Data Analysis in Astronomy. Ettore Majorana International Science Series, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9433-8_3

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  • DOI: https://doi.org/10.1007/978-1-4615-9433-8_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-9435-2

  • Online ISBN: 978-1-4615-9433-8

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